Big O Notation | Time & Space Complexity | Asymptotic Notations | CodeRash with Gaurav

Asymptotic Analysis An algorithm may not have the same performance for different types of inputs. With the increase in the input size, the performance will change. The study of change in performance of the algorithm with the change in the order of the input size is defined as asymptotic analysis. Asymptotic Notations Asymptotic notations are the mathematical notations used to describe the running time of an algorithm when the input tends towards a particular value or a limiting value. Omega Notation (Ω-notation) Omega notation represents the lower bound of the running time of an algorithm. Thus, it provides the best-case complexity of an algorithm. Theta Notation (Θ-notation) Theta notation encloses the function from above and below. Since it represents the upper and the lower bound of the running time of an algorithm, it is used for analyzing the average-case complexity of an algorithm. Big-O Notation (O-notation) Big-O notation represents the upper bound of the running time of an algorithm. Thus, it gives the worst-case complexity of an algorithm. -------------------- Big O notation is used to describe the complexity of an algorithm when measuring its efficiency, which in this case means how well the algorithm scales with the size of the dataset. (Broadly speaking, the process of measuring this type of efficiency is known as "Complexity Analysis," and "Big O" simply refers to the notational system we use to talk about it.) Big O is represented with the following syntax: O(n). The value we're concerned with is between the parentheses and will in most cases include the variable n, which denotes the size of the algorithm's input. In most simple scenarios (i.e., interview problems), the algorithm will be a simple function, and n will typically refer to the size of a collection taken by the function as its input. The value between the parentheses expresses that function's complexity in terms of n. --------------- Timestamps 0:00 - Intro 0:17 - Preface 1:09 - Why do we determine time complexity? 1:51 - Asymptotic Analysis & Notations 3:00 - Three popular asymptotic notations 3:15 - Big Omega, Big Theta & Big O 4:52 - Why Big O is the most common notation? 5:55 - Rules for determining complexity from a polynomial 7:14 - Complexity of simple expressions 8:24 - Complexity of a loop 10:39 - Complexity of nested loops 12:08 - Breaking down the problem, logarithmic complexity 14:00 - Complexity of a code block or an algorithm 16:39 - Comparing Big O complexities 17:48 - Determining space complexity 19:40 - Outro --------------- Buy me a coffee: https://www.patreon.com/coderash https://www.paypal.com/paypalme/gauravbehere --------------- Search keywords: #timecomplexity #bigO #bigOnotation #spacecomplexity #algorithms #datastrcutures #javascript #interview #preparation #javascript #designpatterns #coding #tutorial #coderashwithgaurav javascript,tutorials,array,array methods,es6,map,reduce,filter,includes, array methods explained,all array methods in javascript,javascript interview, javascript, tutorial, javascript, array, inversionOfControl, higherorderfunctions, designpatterns, coding, tutorial, javascript,tutorials,array,array methods,es6, ,javascript interview, programming, #javascript #designpatterns #coding #tutorial #coderashwithgaurav javascript,tutorials,array,array methods,es6,map,reduce,filter,includes, array methods explained,all array methods in javascript,javascript interview, javascript, tutorial, javascript, array, inversionOfControl, higherorderfunctions, designpatterns, coding, tutorial, javascript,tutorials,array,array methods,es6, ,javascript interview, programming #cloningObjects #recursion #JSONStringify #JSONParse, deep cloning objects in javascript, coding,tutorial,javascript,tutorials,javascript interview,programming,react,deep cloning objects in javascript,shallow clone,object destructuring,object assign,lodash clone,Do Not Use JSON Stringify for cloning,coderash with gaurav,JSON Stringify,JSON parse,deep clone,recursion,implement recursion in js,value and reference in js,js tutorial,javascript video,learn js basics,learn javascript,javascript interview questions,front end development basics,JS, asymptotic analysis, big O, time complexity, space complexity, coding,tutorial,javascript,tutorials, timecomplexity,bigO,bigOnotation,spacecomplexity,algorithms,datastrcutures,asymptotic analysis,big O,time complexity,space complexity,asymptotic notations,Time & Space Complexity,problem solving,DSA,data structures,sorting algorithms complexity,how to determine time complexity, Big O Notation | Time & Space Complexity | Asymptotic Notations | CodeRash with Gaurav